# Spring question

1. May 23, 2005

### bullroar_86

one more spring question

A block collides with a spring on a horizontal surface

the block compresses the spring x metres from rest position. What was its speed at the instant of collision

Ok so far I know how to do this question

Ee = Ek
.5kx^2 = .5mv^2

but in this question there is a coefficient of kinetic friction between the block and the surface.. not sure how it fits in.

I'm thinking that it is only affecting the Ee part of the equation..so:

Ee = Ek
.5ukx^2 = .5mv^2

is this right?

2. May 23, 2005

### Curious3141

Well, you can still use conservation of energy, only you have to take into account the work done against friction as well. The friction is a constant force, so things are kept simple.

Do you know $$F_{fr} = \mu N$$, to relate the frictional force to the normal force of the surface on the block ? N, is of course, equal to the weight of the block considering that this is a horizontal surface.

The work done against friction is $$(F_{fr})(x)$$, since x is the distance moved in the direction of the force.

Then just use conservation of energy :

Initial energy of system = Final energy of system

Initial KE of block = Work done against friction (dissipated as heat to surface and block) + Potential Energy stored in spring.

$$\frac{1}{2}mv^2 = \mu mgx + \frac{1}{2}kx^2$$

and express v in terms of $\mu$, m, g, k and x.

Last edited: May 23, 2005